Question

you want to obtain a sample to estimate a population proportion. at this point in time, you have no reasonable preliminary estimation for the population proportion. you would like to be 95% confident that you estimate is within 2% of the true population proportion. how large of a sample size is required

Answer 1

The value is
`n =2401`

Explanation:

From the question we are told that

The margin of error is E = 2%= 0.02

From the question we are told the confidence level is 95% , hence the level of significance is

`\alpha = (100 - 95 ) \%`

=>
`\alpha = 0.05`

Generally from the normal distribution table the critical value of
`(\alpha )/(2)` is

`Z_{(\alpha )/(2) } =  1.96`

Here we are going to assume that the sample proportion is
`\^ p = 0.50`

Generally the sample size is mathematically represented as

`n = [\frac{Z_{(\alpha )/(2) }}{E} ]^2 * \^ p (1 - \^ p )`

=>
`n =[( 1.96 )/( 0.02) ]^2 * 0.5 (1 -0.5  )`

=>
`n =2401`